A control apparatus for an engine, the control apparatus includes an ECU. The ECU is configured to: calculate a normalized intake pressure; calculate a pumping loss torque based on the normalized intake pressure; calculate a first value or a value of a linear function as the normalized intake pressure, the first value is obtained by dividing the intake pressure by the atmospheric pressure; calculate the output value based on the normalized intake pressure and a relational data that associate a normalized output value with the normalized intake pressure; the output value is one of a second value obtained by dividing the pumping loss torque by the atmospheric pressure, a normalized pumping loss torque, a third value obtained by dividing an exhaust pressure by the atmospheric pressure, and a normalized exhaust pressure; and calculate one of the pumping loss torque and the exhaust pressure.